
Re: A New Graph Coloring Conjecture.
Posted:
Jul 1, 2013 7:23 PM


On Saturday, June 29, 2013 12:06:44 AM UTC7, quasi wrote: > >quasi wrote: > > >> bill wrote: > > >> >quasi wrote: > > >> >> bill wrote: > > >> >> > > > >> >> >Forced Five Set: A connected subset of five vertices > > >> >> >(not isomorphic to K5), that cannot be 4colored. > > >> >> > > >> >> With the definition as you've stated it, there's no such > > >> >> thing as a forced 5set. > > >> > > > >> >Am I the only person who would like to see a short > > >> >snappy proof of the 4 CT? > > >> > > >> Sure, that would be nice. > > >> > > >> >I hope to create a simple proof of the Four Color Theorem. > > >> >In this context, I don't think that I will be allowed to > > >> >presume that forced sets do not exist. > > >> > > >> But you _will_ be expected to give a rigorous mathematical > > >> definition of forced sets. You previously said you couldn't > > >> do that. > > > > > >Give me the mathematical definition of an impasse and > > >I will try to adopt it to include forced sets. > > >> > > > >> >I m fairly certain that a forced set may be cited as > > >> >the primary reason for the more common impasses. > > >> > > > >> >In this context; an unresolved impasse in the attempted > > >> >4coloring of a planar graph might be due to the presence > > >> >of a forced set. > > >> > > >> If you can't define forced sets in a way that others can > > >> understand, there's not much chance that anyone would be > > >> able to follow a proposed proof of yours of the 4CT. > > > > > >Can you accept this definition? > > > > > >Consider; > > > > > >Impasse. A difficulty encountered in the attempted > > > four coloring of a graph. > > > > > >Type I " An impasse that is created by the presence of a > > >vertex adjacent to four other vertices, each of which has an > > >assigned color that is different from the assigned color any > > > of the three other vertices". > > > > > >Type II "All other impasses." > > > > No, I don't view that as an acceptable definition. > > > > It appears your concept of a forced 5set in a graph G is a > > set of 5 vertices, S = {a,b,c,d,e} say, such that > > > > (1) Not all vertices of S are adjacent. > > > > (2) One of the vertices of S, e say, is adjacent to the other 4. > > > > (3) Vertices a,b,c,d have already somehow been forced to have > > 4 distinct colors. > > > > My objection is to property (3). It's not clear what it means. > > > > quasi
I hope I finally understand. Tho vertices in 3 are not "forced". Their colors are arbitrarily assigned by the creator of the graph.
bill

